The Sizes and Depletions of the Dust and Gas Cavities in the Transitional Disk J160421.7-213028

5.9 MB·

by  Ruobing Dong

The Sizes and Depletions of the Dust and Gas Cavities in the
Transitional Disk J160421.7-213028
Ruobing Dong1,2, Nienke van der Marel3, Jun Hashimoto4, Eugene Chiang2, Eiji Akiyama5,
Hauyu Baobab Liu6, Takayuki Muto7, Gillian R. Knapp8, Takashi Tsukagoshi9, Joanna
Brown10, Simon Bruderer11, Shin Koyamatsu12, Tomoyuki Kudo13, Nagayoshi Ohashi4,
7
Evan Rich14, Mayama Satoshi15,16, Michihiro Takami17, John Wisniewski14, Yi Yang18,
1
0 Zhaohuan Zhu19, Motohide Tamura4,12
2

n
a
J 1Steward Observatory, University of Arizona, Tucson, AZ, 85721, [email protected]

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2 2Department of Astronomy, University of California at Berkeley, 94720, Berkeley, CA

] 3Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, [email protected]
R
4Astrobiology Center, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588
S
. Japan
h
p 5National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan
-
o
6European Southern Observatory (ESO), Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany
r
t
s 7Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677
a
[
8Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544

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v 9College of Science, Ibaraki University, Bunkyo 2-1-1, Mito, Ibaraki 310-8512, Japan
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8 10Boston Fusion
1
5 11Max-Planck-Institut for Extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
0
12Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-
.
1
ku, Tokyo 113-0033, Japan
0
7 13Subaru Telescope, National Astronomical Observatory of Japan, 650 North Aohoku Place, Hilo, HI
1
: 96720, USA
v
i 14Homer L. Dodge Department of Physics, University of Oklahoma, Norman, OK 73071, USA
X
r 15The Center for the Promotion of Integrated Sciences, The Graduate University for Advanced Stud-
a
ies (SOKENDAI), Shonan International Village, Hayama-cho, Miura-gun, Kanagawa 240-0193, Japan
16Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI),
2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
17InstituteofAstronomyandAstrophysics,AcademiaSinica,POBox23-141,Taipei10617,Taiwan,ROC
18Department of Astronomical Science, The Graduate University for Advanced Studies, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan
19DepartmentofPhysicsandAstronomy,UniversityofNevada,LasVegas,4505SouthMarylandParkway,
Las Vegas, NV 89154
– 2 –
ABSTRACT
We report ALMA Cycle 2 observations of 230 GHz (1.3 mm) dust continuum
emission, and 12CO, 13CO, and C18O J = 2-1 line emission, from the Upper
Scorpius transitional disk [PZ99] J160421.7-213028, with an angular resolution
of ∼0(cid:48)(cid:48).25 (35 AU). Armed with these data and existing H-band scattered light
observations, we measure the size and depth of the disk’s central cavity, and
the sharpness of its outer edge, in three components: sub-µm-sized “small” dust
traced by scattered light, millimeter-sized “big” dust traced by the millimeter
continuum, and gas traced by line emission. Both dust populations feature a
cavity of radius ∼70 AU that is depleted by factors of at least 1000 relative to
the dust density just outside. The millimeter continuum data are well explained
by a cavity with a sharp edge. Scattered light observations can be fitted with
a cavity in small dust that has either a sharp edge at 60 AU, or an edge that
transitions smoothly over an annular width of 10 AU near 60 AU. In gas, the
data are consistent with a cavity that is smaller, about 15 AU in radius, and
whose surface density at 15 AU is 103±1 times smaller than the surface density
at 70 AU; the gas density grades smoothly between these two radii. The CO
isotopologue observations rule out a sharp drop in gas surface density at 30 AU
or a double-drop model as found by previous modeling. Future observations are
needed to assess the nature of these gas and dust cavities, e.g., whether they are
opened by multiple as-yet-unseen planets or photoevaporation.
Subject headings: protoplanetary disks — stars: pre-main sequence— stars: vari-
ables: T Tauri, Herbig Ae/Be — planets and satellites: formation — circumstel-
lar matter — stars:individual ([PZ99] J160421.7-213028)
1. Introduction
Transitional disks are gaseous protoplanetary disks with a central depleted region1 (see
thereviewbyEspaillatetal.2014). Theymarkacrucialphaseindiskevolution,intermediate
between fully gas-rich and gas-depleted systems. Their existence was first suggested by the
distinctivenear-to-mid-infrared(NIR-MIR)dipsintheirspectralenergydistributions(SEDs;
e.g. Strom et al. 1989; Skrutskie et al. 1990; Calvet et al. 2005; Espaillat et al. 2007, 2008),
1Intheliteraturethecentraldepletedregionhasbeencalleda“gap”ora“cavity”,dependingonwhether
the structure extends all the way to the star. In this paper we refer to the structure in J1604 as a cavity.
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and later confirmed by resolved images in NIR scattered light (e.g., Thalmann et al. 2010;
Hashimoto et al. 2012; Mayama et al. 2012; Garufi et al. 2013; Quanz et al. 2013; Avenhaus
et al. 2014a,b; Tsukagoshi et al. 2014) and by resolved mm-wave maps of dust continuum
and gas line emission (e.g. Andrews et al. 2011; Mathews et al. 2012; Tang et al. 2012; Isella
et al. 2013; van der Marel et al. 2013; Fukagawa et al. 2013; van der Marel et al. 2014; P´erez
et al. 2014; Zhang et al. 2014; van der Marel et al. 2015a; Canovas et al. 2015; Hashimoto
et al. 2015).
What opens the cavities in transitional disks? This is still an open question. The leading
hypothesis is dynamical sculpting by planets (or more massive companions) inside the cavity.
Cavity opening is a natural outcome of tidal interactions between a disk and companions
(e.g., Lin & Papaloizou 1993; Artymowicz & Lubow 1994; Bryden et al. 1999; Kley & Nelson
2012). While a single gap opened by one giant planet may be too narrow to account for the
observed cavity sizes in the gas and scattered light, Zhu et al. (2011), Dodson-Robinson &
Salyk (2011), and Dong et al. (2015) explored the possibility of opening a cavity by multiple
giant planets (see also Duffell & Dong 2015). In this scenario, the sharpness of the gas
cavity edge increases with planet mass (e.g., Duffell 2015). Large gradients in gas surface
density can cause the appearance of the cavity (e.g., its size) to depend on wavelength.
Because mm-sized dust particles can pile up at the pressure bump outside the gas cavity
edge (this is called the “dust filtration” effect; Rice et al. 2006; Zhu et al. 2012; Pinilla et al.
2012b,a; de Juan Ovelar et al. 2013), cavities viewed in the mm continuum can be larger
than they appear in scattered light and gas observations. Another consequence of cavity
opening by companions is a reduced accretion rate onto the star, depending on how much
of the disk accretion flow is diverted onto the companions. A small inner disk may remain
if no companions are present there.
Themain alternative non-planet mechanism forclearingbig cavities intransitionaldisks
is photoevaporation (e.g., Clarke et al. 2001; Owen et al. 2010, 2011; Suzuki et al. 2010). In
this scenario, stellar radiation ionizes surface layers of the disk and launches a wind from the
outer disk; if the disk accretion rate is smaller than the wind mass loss rate, the inner disk
is starved and a cavity opens. In this scenario, the cavity edge in both gas and dust tends
to be sharp (e.g., Alexander et al. 2006; Alexander & Armitage 2007), and since the disk is
cleared from the inside out, the accretion on to the star is expected to be very low or zero
(e.g., Owen et al. 2011). Particle trapping at the gap edge can also occur in photoevaporated
cavities.
Other mechanisms for explaining large cavities in observations have also been proposed,
such as grain growth (e.g., Birnstiel et al. 2012) and disk shadowing (e.g., Garufi et al.
2014, for cavity/ring structures seen in scattered light). However, these mechanisms cannot
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reproduce certain observed features in the disks such as cavity edges (Birnstiel et al. 2012;
Dong 2015).
Identifying the origin of the cavity has important implications for disk evolution and
planet formation. Multi-wavelength, spatially resolved observations are needed, as various
cavity formation mechanisms predict different structures for different components, resulting
in different observed disk morphologies at different wavelengths. [PZ99] J160421.7-213028
(hereafterJ1604), atransitionaldiskheavilyscrutinizedinrecentyears, providesanexcellent
case study. This nearly face-on (inclination ∼ 6◦; Mathews et al. 2012) system is located
at ∼145 pc in the ∼5–10 Myr old Upper Scorpius star forming region (de Zeeuw et al.
1999; Pecaut et al. 2012). The central source is a pre-main-sequence star with a spectral
type of K2, an effective temperature of T ∼ 4500K, and a mass M ∼ 1M (Dahm &
eff (cid:63) (cid:12)
Carpenter 2009; Mathews et al. 2012; Carpenter et al. 2014). Its cavity is one of the largest,
extending to ∼70 AU, as vividly revealed in NIR polarized light by Subaru/HiCIAO (H-
band; Mayama et al. 2012) and VLT/SPHERE (R(cid:48)-band; Pinilla et al. 2015). Millimeter
observations using SMA (0.88 mm; Mathews et al. 2012) and ALMA (cycle0, 0.88 mm, band
7; Zhang et al. 2014) have resolved the cavity in dust and CO J =3-2 emission, with angular
resolutions of 0(cid:48)(cid:48).51×0(cid:48)(cid:48).34 and 0(cid:48)(cid:48).73×0(cid:48)(cid:48).46, respectively. As a transitional disk, J1604 has
several peculiar properties. In particular, Owen (2016) pointed out that most transitional
disks can be classified into two classes: one with small holes ((cid:46) 10 AU) and low accretion
rates (< 10−9M yr−1), and another with large holes ((cid:38) 20 AU) and high accretion rates
(cid:12)
∼ 10−8M yr−1. J1604 belongs to neither: it has one of the largest holes, and yet it is hardly
(cid:12)
accreting (Mathews et al. 2012).
In this paper, we present new ALMA Cycle 2 Band-6 (1.3 mm) dust continuum and
J = 2–1 line observations for three CO isotopologues (12CO/13CO/C18O), with an angular
resolution of ∼0(cid:48)(cid:48).25, the highest at mm wavelengths to date. These data, in combination
with a well-sampled SED and resolved observations at 0.6 µm, 1.6 µm, and 0.88 mm, afford
an unprecedentedly detailed examination of a transitional disk. We probe cavity structures
in dust and gas using parametrized axisymmetric disk models and dust and line radiative
transfer simulations (Section 3), to answer three basic questions (Section 4):
1. What are the sizes of the cavities seen in various disk components: “small” sub-µm-
sized dust traced by scattered light, “big” millimeter-sized grains traced by mm dust
continuum emission, and gas traced by CO?
2. How depleted are the cavities in the various disk components?
3. How sharp are the cavity edges in the various disk components?
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A summary and discussion are given at the end (Section 5).
2. ALMA Observations and Data Reduction
J1604 (RA 16:04:21.643, Dec -21:30:28.72; Cutri 2013) was observed with the Atacama
Large Millimeter/submillimeter Array (ALMA) in Band 6 (230 GHz) during ALMA Cycle 2
observations(programID:2013.1.01020.S,PI:T.Tsukagoshi)inJuly2015. Theobservations
were conducted in four spectral windows: two with bandwidths of 117.19 MHz (and channel
widths of 61.035 kHz; equivalent to a velocity resolution of ∼0.08 km s−1) centered on
12CO (2–1) and 13CO (2–1); one with a bandwidth of 468.75 MHz (and a channel width of
0.244 MHz; equivalent to a velocity resolution ∼0.33 km s−1) centered on C18O (2–1); and
a fourth spectral window for continuum observations with a higher sensitivity bandwidth of
1875.00 MHz (and a channel width of 31.250 MHz). The flux and bandpass were calibrated
with the quasar J1517-243, which was used as a bandpass calibrator as well. The gain/phase
calibrator was quasar J1559-2442. The total on-source integration time was 316 seconds.
The data were calibrated with CASA (McMullin et al. 2007, version 4.2) following
the calibration scripts provided by EA-ARC, and then imaged in CASA using the CLEAN
algorithm(Rau&Cornwell2011). Thecontinuumdatawereconcatenatedfromfourspectral
windows providing ∼2.6 GHz of continuum bandwidth.
The continuum data were cleaned using Briggs weighting with a robust factor of 0.5,
and the line data were cleaned using natural weighting, resulting in a beam size of ∼ 0(cid:48)(cid:48).25.
NaturalweightingwaschosenoverBriggsweightingforthelinedataforbetterimagerecovery
as the signal-to-noise ratio is lower for the line data.
The 230 GHz continuum emission and the three CO 2–1 isotopologues 12CO (230.538
GHz), 13CO (220.398677 GHz) and C18O (219.56036 GHz) were all imaged. Table 1 sum-
marizes the continuum and line data.
Figure 1 shows the continuum map, the zero-moment maps (total line intensity) for all
three CO lines, and the first-moment map (the velocity field) in 12CO 2–1. The continuum
is detected with a peak signal-to-noise ratio of 36 (σ=0.11 mJy beam−1), the integrated
line intensities have a peak signal-to-noise ratio of 17, 9 and 6 for 12CO, 13CO and C18O,
respectively, with σ ≈11 mJy km s−1 for the integrated emission. The σ is determined
line
by measuring the standard deviation in a ring outside a 2” radius in the continuum and
zero-moment maps. The first-moment map is consistent with Keplerian rotation, and the
stellar position derived from the first-moment map is RA 16h04m21.638s, Dec -21◦30’28.98”,
consistent with the position of the star in the optical/IR. We derive a position angle of 80◦
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and an inclination of 6◦, consistent with previous estimates based on ALMA Cycle 0 data.
The 230 GHz continuum image shows a narrow, azimuthally symmetric ring, as was found in
previous observations at 345 GHz with lower spatial resolution (Mathews et al. 2012; Zhang
et al. 2014; van der Marel et al. 2015b). The zero moment maps of the CO lines show rings
as well, but with smaller inner radii than the continuum ring, again consistent with previous
findings. Figure 2 shows the azimuthally averaged radial cuts for continuum and integrated
line emission. The inner radii of the 13CO and C18O rings appear slightly larger than that
of the 12CO ring; this may be an effect of their optical depths differing according to their
different abundances. The azimuthally averaged (after correcting for the small inclination)
visibility profiles of both continuum and integrated CO data (bottom panels of Figure 1) are
consistent with ring profiles as well: all profiles show clear nulls, at ∼130 kλ (continuum),
∼170 kλ (12CO), ∼110 kλ (13CO) and ∼110 kλ (C18O).
Non-Keplerian motion may indicate the presence of fast radial flows or disk warps (e.g.,
Rosenfeld et al. 2014; Casassus et al. 2015), or turbulence caused by various instabilities
(e.g., Simon et al. 2015; Flaherty et al. 2015). The ALMA observations of J1604 do not
show any clear indications of non-Keplerian motions, but the nearly face-on orientation of
the disk makes velocity determinations difficult.
3. Modeling
Protoplanetary disks contain gas and variously sized dust grains. Dust dominates the
opacity at nearly all continuum wavelengths. For the purpose of modeling observations,
a disk may be approximated as a three-component system, each primarily responsible for
observationsinonewavelengthrange(e.g.,Dongetal.2012b;vanderMareletal.2015b): (1)
gas — vertically supported by pressure, producing CO emission; (2) sub-micron-sized dust
(hereafter “small” dust) — generally well-mixed with gas in the vertical direction and mainly
responsible for the NIR scattered light; and (3) ∼mm-sized grains (hereafter “big” dust) —
possiblyconcentratedinregionsofhighgaspressureincludingthediskmidplane(Dullemond
& Dominik 2004; D’Alessio et al. 2006; Birnstiel et al. 2010), and mainly responsible for mm
continuum emission. The distribution of small dust grains does affect the mm continuum
by regulating the disk temperature (starlight is intercepted and reprocessed first by small
dust at large altitude); however, this dependence of the mm-wave map on small dust is
relatively minor: midplane temperatures at a given radius vary by a factor of a few at most
using different dust distributions, while surface densities in all three disk components vary
by several orders of magnitudes across the cavity, as we will show.
Weuseradiativetransfersimulationsandparametrizeddiskmodelstoproducesynthetic
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observations and compare them with the data. The models are axisymmetric with as few
radial parameters as needed to match the observations. We do not aim at formally fitting
the observations in a χ2 manner, as this is impractical given the large number of degrees
of freedom; fitting is done by eye instead. We are interested in obtaining rough estimates
for basic properties of the cavity (as viewed in each component): the cavity size, degree of
depletion, and the sharpness of its edge. We employ two radiative transfer tools to produce
synthetic observations. For scattered light, we use the Whitney et al. (2013) Monte Carlo
radiative transfer (MCRT) code; for dust continuum and CO line emission, we use the
physical-chemical DALI code (Bruderer et al. 2012; Bruderer 2013). We treat the small dust
separately from the big dust and the gas in the modeling, and largely follow the procedures
described by Dong et al. (2012a) for scattered light and van der Marel et al. (2016) for mm
continuum and line emission.
The disk starts from the dust sublimation radius R , corresponding to a temperature
sub
of ∼1500 K (∼0.055 AU for J1604), and extends to an outer radius R . For the central
out
source, we use apre-main sequencestar ofspectral type K2, radius 1.4R , mass1.0 M , and
(cid:12) (cid:12)
temperature 4500 K. The star is not known to be accreting (M˙ < 10−11M /yr; Mathews
(cid:12)
et al. 2012). Our model’s surface density profile Σ(R) divides into an outer disk and a
depleted inner disk for all three components, as illustrated in Figure 3:
(cid:40)δ (R)Σ (cid:0)Rc(cid:1)γe−R/Rc,R ≤ R Cavity
Σ(R) = cav 0 R cav (1)
Σ (cid:0)Rc(cid:1)γe−R/Rc,R < R ≤ R Outer Disk
0 R cav out
where the exponential length scale R , power-law index γ, cavity depletion factor δ (R),
c cav
and cavity radius R are parameters specific to each of the three disk components (small
cav
dust, big dust, and gas). For small dust we introduce an additional rim structure from R
sub
to R to account for possible NIR excess:2 the surface density of small dust inside the rim
rim
is given by δ Σ (cid:0)Rc(cid:1)γe−R/Rc. Note that δ can vary with radius. In some of our models
rim 0 R cav
we will set δ to be constant, while in others we will allow it vary with radius to introduce
cav
additional structure.
In the vertical direction z, strongly irradiated (i.e., passive) protoplanetary disks are
roughlyisothermal, exceptinthetenuousupperlayers(Chiang&Goldreich1997;Dullemond
2J1604hasbeenlabeledapossiblevariablesourcebyDahm&Carpenter(2009); theIRACdataindicate
no NIR excess, while the Spitzer IRS spectrum indicate a NIR excess. The later WISE data at 3.4 and 4.6
µm (Cutri 2012) are consistent with the IRS spectrum but not the IRAC photometry. We adopt the WISE
and IRS data in this paper (the IRAC data are not plotted in Figure 3).
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2002). In hydrostatic equilibrium, the vertical gas density follows a Gaussian profile:
Σ(R)
ρ(R,z) = √ e−z2/2h2, (2)
2πh
where h is the scale height. The big grains tend to settle to the midplane; we assume their
vertical distribution also obeys a Gaussian but with a smaller h. Radially, the scale height
is assumed to vary with radius as
h ∝ Rψ, (3)
where ψ is a component-dependent constant.
We adopt the interstellar medium dust model of Kim et al. (1994) for small dust (com-
posed of silicate, graphite, and amorphous carbon) with a size distribution that runs from
∼0.002µm to ∼0.25µm. As J1604 is nearly face-on, the scattering angle everywhere in the
scattered light image is close to 90◦. We assume the Andrews et al. (2011) big dust model
for our big dust, which has a minimum size of 0.005 µm and a maximum size of 1 mm with a
power law differential size (s) distribution n(s) ∝ s−3.5. Mie scattering is assumed for both
dust populations.
ForthemodelingoftheCOisotopologues,theDALIcode(Brudereretal.2012;Bruderer
2013) is used. DALI is a physical-chemical modeling code which solves the heating-cooling
balance of the gas and chemistry simultaneously to determine the gas temperature, molec-
ular abundances and molecular excitation in every position in the disk for a given density
structure. DALI uses a chemical reaction network of about 110 species and 1500 reactions,
including basic grain-surface reactions (freeze-out, sublimation and hydrogenation). DALI
is required for proper interpretation of CO emission for several reasons: the gas and dust
temperature are decoupled in disks, especially inside and at the cavity edges; the local CO
abundance w.r.t. H is lowered due to photodissociation and freeze-out and is thus not a
2
direct gas density tracer; CO is formed and destroyed through various chemical reactions
depending on the local conditions in the disk. DALI has been used to interpret several
transition disks in spatially resolved CO observations (Bruderer et al. 2014; van der Marel
et al. 2015b, 2016). The full details on the DALI model are discussed in these papers as
well. The assumed abundance ratios of the CO isotopologues in DALI are 12CO/13CO=77
and 12CO/C18O=560. The effects of isotope-selective photodissociation (e.g., Miotello et al.
2014) have been checked but these do not significantly change the emission for our fiducial
model.
In total, there are 23 parameters: Σ (equivalent to the total disk mass), R , R ,
0 c out
γ, ψ, R , and δ for each of the 3 components, plus δ and R for the small dust.
cav cav rim rim
We use subscripts “gas,” “small-dust,” and “big-dust” to indicate each component. We
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are mainly interested in the cavity size, depletion, and edge structure for each of the three
components. These parameters largely determine the cavity morphology in observations,
while experiments have shown that our data are insensitive to many of the other parameters
(Dong et al. 2012b,a; van der Marel et al. 2015b, 2016).
From our model we generate the SED, and images in H-band polarized light, mm
continuum, and 12CO/13CO/C18O J =2–1 emission. For scattered light we use the Sub-
aru/HiCIAO image by Mayama et al. 2012 (data taken as part of the SEEDS planet and
disk survey; Tamura 2009), and for continuum and line emission we use the ALMA Cycle 2
data presented in this paper. For the H-band images, we convolve the full resolution model
images with the observed HiCIAO point spread function to achieve the appropriate angular
resolution. Synthetic ALMA images are convolved with the ALMA angular resolution as
given in Table 1. Also, we calculate the visibility profiles directly from the integrated gas
moment maps and continuum images and compare these with the observed visibility profiles.
4. Disk Properties
In this section, we first present a fiducial model that fits all the observations reasonably
well (Section 4.1). We then vary the sizes (4.2), depletion factors (4.3), and sharpnesses of
the cavity edges (4.4) to explore the uncertainties.
4.1. The Fiducial Model
Table 2 lists the parameters of the fiducial model as portrayed in Figures 3–6. Figure 3
shows the model surface density radial profiles for the three components and compares
the global SED of the model with observations. Figure 4 compares the H-band polarized
intensity images; Figure 5 the visibilities of the models and data for the line emission and
mm continuum; and Figure 6 the model and observed maps for the same. The photometry
and the IRS spectrum used to construct the SED are listed in Table 3. The fiducial model
qualitatively reproduces the SED, the image morphology at each wavelength, the radial
profile of the scattered light, the mm visibilities, and the CO spectrum (none of the synthetic
observations has been rescaled in flux). The fiducial model is also consistent with ALMA
Cycle 0 345 GHz continuum and 12CO J=3-2 data (not shown).
The total dust mass in the model is 0.066 M (0.013 M in small dust and 0.053 M
J J J
in big dust, and the total gas mass is 2.5 M , resulting in a global gas-to-dust-mass ratio
J
of ∼38:1. The scattered light and dust continuum observations are consistent with the
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simplest model — an outer disk, a cavity that is completely empty (except possibly for a
< 0.1 AU inner disk in small dust, see below), and a sharp cavity edge. For the small
dust we have an inner rim extending from R = 0.055 AU to R =0.07 AU, included to
sub rim
account for the occasional NIR excess (see footnote 2). Note that detailed SED fitting is
beyond the scope of this paper. In reality grain sizes can vary across the disk, and relaxing
our assumption of a single grain size distribution can help on the SED fitting. This inner
rim does not affect the three resolved observations discussed here. The cavity sizes in the
two dust populations differ slightly (R = 60 AU while R = 70 AU);
cav,small−dust cav,big−dust
however, we will see later that the difference is insignificant. For the gas, the simple cavity
model — a gas cavity of 30 AU with a sharp edge, used by van der Marel et al. (2015b) to fit
the lower resolution Cycle 0 12CO data — does not fit the new ALMA 13CO and C18O data
(Section 4.4). In order to fit all three isotopologues simultaneously, a smooth rather than a
sharp cutoff at the gas cavity edge is required. We therefore add to the fiducial model for gas
by introducing a smooth exponential drop-off in surface density between the big-dust cavity
radius R = 70 AU and the gas cavity radius R = 15 AU. A full description
cav,big−dust cav,gas
of the gas surface density in the fiducial model is:
δcav,gas(R)Σ0,gas(cid:16)RcR,gas(cid:17)γgase−R/Rc,gas R ≤ Rcav,gas Cavity

Σgas(R) = Σgas(Rcav,big−dust)·e(R−Rcav,big−dust)/w Rcav,gas ≤ R ≤ Rcav,big−dust Transition Region
Σ0,gas(cid:16)RcR,gas(cid:17)γgase−R/Rc,gas Rcav,big−dust ≤ R ≤ Rout,gas Outer Disk
(4)
where w is
R −R
cav,big−dust cav,gas
w = . (5)
ln[Σ (R )/Σ (R )]
gas cav,big−dust gas cav,gas
As a point of clarification, the free parameters in the above equations are δ , Σ ,
cav,gas 0,gas
R , γ , R , and R . We connect the gas surface density to R so
c,gas gas cav,gas cav,big−dust cav,big−dust
that the gas pressure reaches a local maximum there — see Figure 3. This is motivated by
dust filtration, which predicts that mm-sized particles drift toward the pressure peak. Inside
R , δ = 10−5 — note that this implies the gas surface density at 15 AU is about
cav,gas cav,gas
10−3 of the value at 70 AU. The gas-to-dust ratio is 50:1 in the outer disk. We note that our
fiducial model overproduces the 13CO and C18O emission in the outer disk (at the shortest
baselines) compared to the data, but we do not consider this discrepancy further as our focus
in this paper is on the inner cavity.
We emphasize that the fiducial model does not provide a unique fit to the data. With
the exceptions of cavity radius and depth, as discussed below, the constraints on many other
parameters are rather weak (e.g., Dong et al. 2012a,b; van der Marel et al. 2015b). Also,
local non-axisymmetric features, such as the dip on the ring at H-band, are not reproduced